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This paper presents a procedure whereby the dynamic soil constants required for the accurate prediction of the natural frequencies of a foundation-soil system may be determined. The foundation-soil system is treated by considering the foundation mass to be supported by a truncated pyramid of “soil springs.” By the use of this analogy, the effect on the spring constants of the size and shape of the contact area and the effect of increasing soil modulus with depth may be evaluated. The analogy further permits the computation of the effective or apparent mass of soil moving with the foundation. Analytical expressions are derived for the dynamic soil constants and are presented in graphical form to permit rapid calculation. The equations of motion for a block foundation are next discussed and sample calculations for determining the natural frequencies of a typical foundation are shown. In conclusion, the accuracy of the procedure is demonstrated by comparing computed frequencies with the frequencies observed on experimental model foundations.
Associate Professor of Civil Engineering, University of Missouri, Columbia, Mo